What is the maximum number of nodes in an AVL tree of height h?
Practice Questions
Q1
What is the maximum number of nodes in an AVL tree of height h?
2^h - 1
2^(h+1) - 1
Fibonacci(h+2) - 1
h^2
Questions & Step-by-Step Solutions
What is the maximum number of nodes in an AVL tree of height h?
Step 1: Understand what an AVL tree is. An AVL tree is a type of binary search tree that maintains balance, meaning the heights of the two child subtrees of any node differ by at most one.
Step 2: Know what height means. The height of a tree is the number of edges on the longest path from the root to a leaf.
Step 3: Recognize that the maximum number of nodes in an AVL tree increases as the height increases.
Step 4: Learn about Fibonacci numbers. The Fibonacci sequence starts with 0 and 1, and each subsequent number is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8, 13, ...
Step 5: The formula for the maximum number of nodes in an AVL tree of height h is Fibonacci(h + 2) - 1. This means you find the Fibonacci number at position (h + 2) and then subtract 1.
Step 6: For example, if h = 3, calculate Fibonacci(3 + 2) = Fibonacci(5) which is 5. Then subtract 1 to get 4, which is the maximum number of nodes in an AVL tree of height 3.
